x*x-45x-9000=0

Solution for x*x-45x-9000=0 equation:

x*x-45x-9000=0

We add all the numbers together, and all the variables

-45x+x*x-9000=0

Wy multiply elements

x^2-45x-9000=0

a = 1; b = -45; c = -9000;
Δ = b2-4ac
Δ = -452-4·1·(-9000)
Δ = 38025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{38025}=195$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-195}{2*1}=\frac{-150}{2}
=-75
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+195}{2*1}=\frac{240}{2}
=120
$